Automated analysis of the trajectories of stochastic dynamical systems under uncertainty

Abstract

The aim is to develop a method of computer analysis of stochastic trajectories of dynamical systems, based on the proposed by member. cor. the USSR Academy of Sciences A.A. Vavilov principle consistent disclosure of the topological, structural, parametrical and signal uncertainties. Identification of the model parameters is carried out using the method of weighted least squares, and a modified weighting function on the basis of solving the inverse problem with constraints on the parameter values. For structural identification a modified Akaike criterion is used with a weighted sum of squared residuals (WRSS) and the adjusted coefficient of determination. To split mixed trajectories with Brownian diffusion and directed movement is used segmentation method based on approximation of a piecewise - linear splines. The method is implemented in a network software system. Experimental results demonstrate increasing efficiency of the trajectories analysis of stochastic dynamical systems under uncertainty.